Theorems · Theorem · measure theory

MeasureTheory.Measure.map_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {f : α → β}, Measurable f → ∀ {s : Set β}, MeasurableSet s → (MeasureTheory.Measure.map f μ) s = μ (f ⁻¹' s)

Defined in

Mathlib.MeasureTheory.Measure.Map

Cited by

139 results in Mathlib

Foundations

Depth 199 from the axioms, rests on 4,758 definitions · uses propext, Classical.choice, Quot.sound